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How many zeros does 100! end with? 20 24 25 30 32 from the

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Director
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How many zeros does 100! end with? 20 24 25 30 32 from the [#permalink] New post 09 Dec 2004, 20:55
How many zeros does 100! end with?

20
24
25
30
32

from the challenge archive.


pls explain answer

ty!
Manager
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 [#permalink] New post 10 Dec 2004, 03:12
My answer is B 24
If it is correct, I'll explain why :)
CIO
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 [#permalink] New post 10 Dec 2004, 12:20
I think it's 20.

every zero is going to come from another multiple of 10 in the mix. So 100,90,80,70,60,50,40,30,20,10 each contribute one zero to the total. We now have 10 zeros.

But ten comes from 2x5, so for every 5 that's in this thing, if there's an even to multiply it by, then there's another 10. so 95, 85, 75, 65, 55, 45, 35, 25, 15, 5 all contribute a 5, and there are definately enough even numbers to multiply them all by, so that's another 10 zeros.

Since there's no other way to get zeros, there are 20 contributers, and 20 zeros all together.
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 [#permalink] New post 10 Dec 2004, 12:38
1) 100,90,80,70,60,50,40,30,20,10 ELEVEN ZEROS from here
2) 25,50,75 THREE MORE ZEROS
because 25=5x5
50=10x5
75=5x5x5
So 24 total I think :-D
CIO
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 [#permalink] New post 10 Dec 2004, 12:45
lovely_baby wrote:
1) 100,90,80,70,60,50,40,30,20,10 ELEVEN ZEROS from here
2) 25,50,75 THREE MORE ZEROS
because 25=5x5
50=10x5
75=5x5x5
So 24 total I think :-D


definately. i missed all those. good catch!
  [#permalink] 10 Dec 2004, 12:45
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